test(console): pin system-turn dedupe wiring on both read paths

The live-SSE/history system-turn dedupe (renderedSystemEventIds /
_renderedSystemEventIds) was already in place on both panes and merged
to main (21af6c4 aligned the persisted row event_id with its SSE event;
09e41d1 added the belt-and-braces Set on the coordinator). The existing
pin tests only assert the Set's .has()/.add()/.clear() symbols appear
somewhere in the file, so a refactor that keeps the Set but short-circuits
the live-handler consultation (guard -> false) re-opens the double-render
while the pins stay green.

Scope the new assertions to their blocks: the live system_turn case must
CONSULT and RECORD against the Set, and the history render path
(replayHistory / refetchHistory's system-role branch) must record each
replayed row's event_id. Bounded at the next switch case rather than the
first break; the dedup-skip path itself breaks before the .add(), so a
break-bounded slice would drop the record half.

Verified the new slice checks fail on a dedupe-neutered factory (a
headless-Chrome harness driving the real createCoordinatorPane confirms
that neutering produces two rendered nodes for one event id; intact code
renders one, and the no-event-id legacy path still renders both).

tests/test_app_js.py

@@ -285,6 +285,33 @@ def test_system_turn_dedups_against_history_by_event_id() -> None:
         "replayHistory (and the live handler) must record system-turn ids for the dedup set."
     )
 
+    # Pin the wiring on BOTH read paths, scoped to its method — a refactor that
+    # keeps the Set but drops the live-handler consultation (or the
+    # replayHistory-side record) silently re-opens the double-render while the
+    # file-global checks above still pass.
+    live_start = body.index('case "system_turn":')
+    # End at the NEXT switch case, not the first ``break;`` — the dedup-skip
+    # path breaks before the ``.add(``, so a ``break;``-bounded slice would
+    # drop the record half and false-fail the ``.add(`` assertion below.
+    live_end = body.index('\n      case "', live_start + 1)
+    live_block = body[live_start:live_end]
+    assert re.search(r"_renderedSystemEventIds[\s\S]*?\.\s*has\(", live_block), (
+        "the live system_turn handler must CONSULT the dedup set (skip an id "
+        "already painted from /history), not merely reference the Set elsewhere."
+    )
+    assert re.search(r"_renderedSystemEventIds[\s\S]*?\.\s*add\(", live_block), (
+        "the live system_turn handler must RECORD the id it renders so a later "
+        "/history re-render (clear_ui) doesn't repaint it."
+    )
+
+    replay_start = _pane_method_offset(body, "replayHistory")
+    replay_end = _pane_method_offset(body, "_attachRetryToLastAssistant")
+    replay_block = body[replay_start:replay_end]
+    assert re.search(r"_renderedSystemEventIds[\s\S]*?\.\s*add\(", replay_block), (
+        "replayHistory must record each replayed system row's event_id so the "
+        "live system_turn handler can dedup against it."
+    )
+
 
 def test_retry_walk_skips_operator_context_cards() -> None:
     """Interactive twin of the coord retry-skip guard.

tests/test_coordinator_page.py

@@ -401,6 +401,38 @@ def test_coord_dedups_system_turn_against_history_by_event_id():
         "false-skip after clear_ui / replay_truncated."
     )
 
+    # The seam must be wired on BOTH read paths, not merely present somewhere
+    # in the file — a refactor that keeps the Set but drops the live-handler
+    # consultation (or the history-side record) silently re-opens the
+    # double-render. Scope each assertion to its block so the wiring, not the
+    # bare symbol, is pinned. (A dedupe-neutered factory — guard short-circuited
+    # to ``false`` — still contains ``renderedSystemEventIds.has(`` and so
+    # passes the file-global checks above; these slice checks catch it.)
+    sys_case = body.index('case "system_turn":')
+    # End at the NEXT switch case, not the first ``break;`` — the dedup-skip
+    # ``...has(sysEid)) break;`` is itself a break that precedes the ``.add(``,
+    # so a ``break;``-bounded slice would drop the record half.
+    sys_case_end = body.index('\n      case "', sys_case + 1)
+    live_block = body[sys_case:sys_case_end]
+    assert "renderedSystemEventIds.has(" in live_block, (
+        "the live system_turn handler must CONSULT the dedup set (skip an id "
+        "already painted from /history) — not just reference the Set elsewhere."
+    )
+    assert "renderedSystemEventIds.add(" in live_block, (
+        "the live system_turn handler must RECORD the id it renders so a later "
+        "/history re-render (clear_ui) doesn't repaint it."
+    )
+
+    # The history render path must seed the set from each replayed system row's
+    # event_id, so a subsequent live replay of the same id is skipped.
+    assert 'role === "system"' in body
+    sys_replay = body.index('role === "system"', body.index("refetchHistory"))
+    replay_window = body[sys_replay : sys_replay + 600]
+    assert "renderedSystemEventIds.add(" in replay_window, (
+        "the history render's system-role branch must record each replayed "
+        "turn's event_id so the live system_turn handler can dedup against it."
+    )
+
 
 def test_coord_retry_walk_skips_operator_context_cards():
     """Retry must NOT regenerate a stale assistant turn when the last DOM row is